Near soft-output maximum-likelihood detection for multiple-input multiple-output systems

ABSTRACT

Systems and methodologies are described that provide low-complexity soft-output detection for MIMO communication systems. Looping can be performed over a set of constellation points per spatial stream to obtain distance metrics for each of a series of transmitted streams, for which values for the other transmitted streams can be estimated using a MIMO channel matrix and a sub-optimal MIMO algorithm. Examples of MIMO algorithms that can be utilized include Per-Stream List Detection (PSLD), Lattice-Reduced Detection (LRD), and a Guided-M Algorithm. Performance can be further improved by pre-processing the MIMO channel matrix and/or by utilizing techniques for Enhanced Metric Usage (EMU).

BACKGROUND

1. Field

The present disclosure relates generally to wireless communications andmore specifically to techniques for signal detection in a wirelesscommunication system.

2. Background

Wireless communication systems have become a prevalent means by which amajority of people worldwide have come to communicate. This is due inlarge part to the fact that recent advances in wireless communicationtechnology have considerably improved the ability of such systems tocarry data relating to voice, video, packet data, broadcast, messaging,and other services used in communication. In particular, multiple-inputmultiple-output (MIMO) communication systems are receiving increasedattention due to their ability to improve the capacity of a wirelesscommunication system through the use of multiple antennas forsimultaneously transmitting and receiving data. Using a MIMOcommunication system, data can be divided into multiple streams, whichcan be sent and received simultaneously to improve system capacitywithout requiring significant additional spectrum or power.

In typical MIMO communication systems, data is transmitted by dividingthe data into streams, grouping bits in each stream, mapping each groupof bits to constellation points, and then transmitting the streams viamultiple transmit antennas as modulated carrier waves based on theconstellation points mapped for each stream. Once transmitted, the datapasses through an effective MIMO channel, after which resulting spatialstreams are received by multiple antennas at a receiver. ConventionalMIMO receivers then employ a variety of signal detection techniques toobtain data from streams received at receive antennas. Once suchtechnique, Soft-Output Maximum-Likelihood Detection (SOMLD), can obtainthe expected value of a detected transmitted bit as well as thelikelihood that the expected value is correct. Conventional SOMLDtechniques require looping over all constellation points used by thetransmitter for each transmitted stream and determining a distancemetric for each constellation point to find the likelihood of each bitin the streams. However, to determine optimal distance metrics inconventional SOMLD, additional looping is required over allconstellation points for all other streams, effectively requiringlooping over all possible combinations of constellation points for allstreams. This procedure has exponential computational complexity, whichmakes it prohibitively costly for many applications, includingapplications that could benefit from soft-output detection. Thus, thereexists a need in the art for low-complexity techniques that achieveMaximum-Likelihood-Detection (MLD) performance or near-MLD performancefor hard-decision output detection or that achieve SOMLD performance ornear-SOMLD performance for soft-decision output signal detection in MIMOcommunication systems.

SUMMARY

The following presents a simplified summary of the disclosed embodimentsin order to provide a basic understanding of such embodiments. Thissummary is not an extensive overview of all contemplated embodiments,and is intended to neither identify key or critical elements nordelineate the scope of such embodiments. Its sole purpose is to presentsome concepts of the disclosed embodiments in a simplified form as aprelude to the more detailed description that is presented later.

The described embodiments mitigate the above-mentioned problems byproviding low-complexity techniques for maximum-likelihood detection inMIMO communication systems that yield close-to-optimal distance metricsfor soft-output generation. More particularly, systems and methodologiesdescribed herein can loop over all constellation points per spatialstream to obtain distance metrics for each stream. Instead of performingadditional looping for all other streams within the calculations for aparticular stream, values for the other streams that yieldclose-to-optimal distance metrics can be estimated using a MIMO channelmatrix and a sub-optimal MIMO algorithm such as Per-Stream ListDetection (PSLD), Lattice-Reduced Detection (LRD), or a Guided-MAlgorithm as described herein. Performance can be further improved bypre-processing the MIMO channel matrix and/or by utilizing EnhancedMetric Usage (EMU) as further described herein.

According to an aspect, a method for generating soft-decision outputvalues for a set of transmitted spatial streams in a multiple-inputmultiple-output (MIMO) communication system is described herein. Themethod can comprise looping over a plurality of constellation points forrespective transmitted spatial streams to estimate values for othertransmitted streams based at least in part on a sub-optimal MIMOalgorithm. The method can further comprise determining a set of distancemetrics as values of the plurality of constellation points for therespective transmitted spatial streams. In addition, the method cancomprise generating soft-decision outputs for the respective transmittedstreams based at least in part on the set of distance metrics.

Another aspect relates to a wireless communications apparatus that caninclude a memory that stores data relating to a set of received streamsand a matrix corresponding to a channel through which a set oftransmitted streams corresponding to the set of received streams werecommunicated. The wireless communications apparatus can further comprisea processor configured to loop over one or more constellation points forrespective transmitted streams to determine estimated values for othertransmitted streams and corresponding distance metrics using the matrixand a sub-optimal MIMO algorithm and to generate soft-decision outputsfor the respective transmitted streams as log-likelihood ratios of thedetermined distance metrics.

Yet another aspect relates to an apparatus that provides low-complexitynear-soft-output maximum likelihood detection for a series oftransmitted streams. The apparatus can comprise means for looping over aset of constellation points for respective transmitted streams toestimate other elements using a sub-optimal MIMO algorithm. In addition,the apparatus can comprise means for determining distance metrics forthe respective transmitted streams over the set of constellation points.Further, the apparatus can comprise means for obtaining soft-decisionoutputs for respective bits in the transmitted streams based on thedetermined distance metrics.

Still another aspect relates to a computer-readable medium having storedthereon computer-executable instructions for soft value generation for aset of transmitted streams in a wireless communication system. Theinstructions can comprise utilizing a channel matrix and a sub-optimalMIMO algorithm iteratively over a set of possible constellation pointsfor respective transmitted streams in the set of transmitted streams toestimate corresponding values for other transmitted streams in the setof transmitted streams and to determine corresponding distance metrics.The instructions can additionally include obtaining soft-decisionoutputs for respective bits in the set of transmitted streams based onthe distance metrics.

In accordance with another aspect, a processor is described herein thatcan execute computer-executable instructions for low-complexitysoft-output detection in a MIMO receiver. The instructions can includelooping over one or more constellation points for respective transmittedstreams to estimate other elements and to determine correspondingdistance metrics using a sub-optimal MIMO algorithm. Additionally, theinstructions can comprise obtaining soft-decision outputs by calculatinglog-likelihood ratios for respective bits in the transmitted streamsbased on the distance metrics.

An additional aspect relates to a method for generating soft-decisionoutput values for a set of transmitted spatial streams in acommunication system. The method can comprise looping over a pluralityof constellation points for respective transmitted spatial streams toestimate values for other transmitted streams based at least in part ona single-input single-output (SISO) algorithm. Further, the method caninclude determining a set of distance metrics as values of the pluralityof constellation points for the respective transmitted spatial streams.The method can additionally include generating soft-decision outputs forthe respective transmitted streams based at least in part on the set ofdistance metrics.

To the accomplishment of the foregoing and related ends, one or moreembodiments comprise the features hereinafter fully described andparticularly pointed out in the claims. The following description andthe annexed drawings set forth in detail certain illustrative aspects ofthe disclosed embodiments. These aspects are indicative, however, of buta few of the various ways in which the principles of various embodimentsmay be employed. Further, the disclosed embodiments are intended toinclude all such aspects and their equivalents.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a wireless multiple-access communication system inaccordance with various aspects set forth herein.

FIG. 2 is a block diagram of a multiple-input multiple-output (MIMO)wireless communication system that facilitates transmission anddetection of spatial data streams in accordance with various aspectsdescribed herein.

FIG. 3 illustrates an example signal detection component that can beutilized in a MIMO communication system in accordance with variousaspects.

FIG. 4 is a flow diagram of a methodology for low-complexitynear-soft-output maximum likelihood detection (near-SOMLD) in a MIMOcommunication system.

FIG. 5 is a flow diagram of a methodology for near-SOMLD in a MIMOcommunication system using a Per-Stream List Detection algorithm.

FIG. 6 is a flow diagram of a methodology for near-SOMLD in a MIMOcommunication system using a Lattice-Reduced Detection algorithm.

FIG. 7 is a flow diagram of a methodology for near-SOMLD in a MIMOcommunication system using a Guided-M algorithm.

FIG. 8 is a flow diagram of a methodology for low-complexity soft-outputdetection in a MIMO communication system with Enhanced Metric Usage.

FIG. 9 is a block diagram illustrating an example wireless communicationsystem in which one or more embodiments described herein may function.

FIG. 10 is a block diagram of a system that coordinates modulation andtransmission of spatial data streams in accordance with various aspects.

FIG. 11 is a block diagram of a system that coordinates reception anddetection of spatial data streams in accordance with various aspects.

FIG. 12 is a block diagram of an apparatus that provides nearsoft-output maximum likelihood detection in accordance with variousaspects.

FIG. 13 is a block diagram of an apparatus that provides nearsoft-output maximum likelihood detection via MIMO channel matrixpre-processing and utilization of sub-optimal MIMO algorithms inaccordance with various aspects.

FIG. 14 is a block diagram of an apparatus that provides nearsoft-output maximum likelihood detection with Enhanced Metric Usage inaccordance with various aspects.

DETAILED DESCRIPTION

Various embodiments are now described with reference to the drawings,wherein like reference numerals are used to refer to like elementsthroughout. In the following description, for purposes of explanation,numerous specific details are set forth in order to provide a thoroughunderstanding of one or more aspects. It may be evident, however, thatsuch embodiment(s) may be practiced without these specific details. Inother instances, well-known structures and devices are shown in blockdiagram form in order to facilitate describing one or more embodiments.

As used in this application, the terms “component,” “module,” “system,”and the like are intended to refer to a computer-related entity, eitherhardware, firmware, a combination of hardware and software, software, orsoftware in execution. For example, a component may be, but is notlimited to being, a process running on a processor, a processor, anobject, an executable, a thread of execution, a program, and/or acomputer. By way of illustration, both an application running on acomputing device and the computing device can be a component. One ormore components can reside within a process and/or thread of executionand a component may be localized on one computer and/or distributedbetween two or more computers. In addition, these components can executefrom various computer readable media having various data structuresstored thereon. The components may communicate by way of local and/orremote processes such as in accordance with a signal having one or moredata packets (e.g., data from one component interacting with anothercomponent in a local system, distributed system, and/or across a networksuch as the Internet with other systems by way of the signal).

Furthermore, various embodiments are described herein in connection witha wireless terminal and/or a base station. A wireless terminal may referto a device providing voice and/or data connectivity to a user. Awireless terminal may be connected to a computing device such as alaptop computer or desktop computer, or it may be a self containeddevice such as a personal digital assistant (PDA). A wireless terminalcan also be called a system, a subscriber unit, a subscriber station,mobile station, mobile, remote station, access point, remote terminal,access terminal, user terminal, user agent, user device, or userequipment. A wireless terminal may be a subscriber station, wirelessdevice, cellular telephone, PCS telephone, cordless telephone, a SessionInitiation Protocol (SIP) phone, a wireless local loop (WLL) station, apersonal digital assistant (PDA), a handheld device having wirelessconnection capability, or other processing device connected to awireless modem. A base station (e.g., access point) may refer to adevice in an access network that communicates over the air-interface,through one or more sectors, with wireless terminals. The base stationmay act as a router between the wireless terminal and the rest of theaccess network, which may include an Internet Protocol (IP) network, byconverting received air-interface frames to IP packets. The base stationalso coordinates management of attributes for the air interface.

Moreover, various aspects or features described herein may beimplemented as a method, apparatus, or article of manufacture usingstandard programming and/or engineering techniques. The term “article ofmanufacture” as used herein is intended to encompass a computer programaccessible from any computer-readable device, carrier, or media. Forexample, computer readable media can include but are not limited tomagnetic storage devices (e.g., hard disk, floppy disk, magnetic strips. . . ), optical disks (e.g., compact disk (CD), digital versatile disk(DVD) . . . ), smart cards, and flash memory devices (e.g., card, stick,key drive . . . ).

Various embodiments will be presented in terms of systems that mayinclude a number of devices, components, modules, and the like. It is tobe understood and appreciated that the various systems may includeadditional devices, components, modules, etc. and/or may not include allof the devices, components, modules etc. discussed in connection withthe figures. A combination of these approaches may also be used.

In addition, while various embodiments are generally presented herein inthe context of a wireless communication system, it should be appreciatedthat the systems and methodologies described herein can be utilized inconnection with any suitable system and/or application that can employwired and/or wireless communications. For example, various embodimentsdescribed herein can be used in MIMO systems employing IEEE 802.11n or asimilar standard, Multi-User Detection applications, multi-mode fiberand fiber-optic applications, Ethernet communication systems and/orapplications that can operate at 1 G, 10 G, or another suitable rate,and/or any other suitable communication systems or applications.Further, it should be appreciated that all such systems and applicationsare intended to fall within the scope of the hereto appended claims.

Referring now to the drawings, FIG. 1 is an illustration of a wirelessmultiple-access communication system in accordance with various aspects.In one example, an access point 100 (AP) includes multiple antennagroups. As illustrated in FIG. 1, one antenna group can include antennas104 and 106, another can include antennas 108 and 110, and another caninclude antennas 112 and 114. While only two antennas are shown in FIG.1 for each antenna group, it should be appreciated that more or fewerantennas may be utilized for each antenna group. In another example, anaccess terminal 116 (AT) can be in communication with antennas 112 and114, where antennas 112 and 114 transmit information to access terminal116 over forward link 120 and receive information from access terminal116 over reverse link 118. Additionally and/or alternatively, accessterminal 122 can be in communication with antennas 104 and 106, whereantennas 104 and 106 transmit information to access terminal 122 overforward link 126 and receive information from access terminal 122 overreverse link 124. In accordance with one aspect, access terminals 116and 122 can have multiple antennas, with which multiple-inputmultiple-output (MIMO) communication can be established between accessterminals 116 and 122 and access point 100 over respective forward links120 and 126 and/or reverse links 118 and 124. Further, in a frequencydivision duplex (FDD) system, communication links 118, 120, 124 and 126can use different frequencies for communication. For example, forwardlink 120 may use a different frequency then that used by reverse link118.

Each group of antennas and/or the area in which they are designed tocommunicate can be referred to as a sector of the access point. Inaccordance with one aspect, antenna groups can be designed tocommunicate to access terminals in a sector of areas covered by accesspoint 100. In communication over forward links 120 and 126, thetransmitting antennas of access point 100 can utilize beamforming inorder to improve the signal-to-noise ratio of forward links for thedifferent access terminals 116 and 122. Also, an access point usingbeamforming to transmit to access terminals scattered randomly throughits coverage causes less interference to access terminals in neighboringcells than an access point transmitting through a single antenna to allits access terminals.

An access point, e.g., access point 100, can be a fixed station used forcommunicating with terminals and can also be referred to as a basestation, a Node B, and/or other suitable terminology. In addition, anaccess terminal, e.g., an access terminal 116 or 122, can also bereferred to as a mobile terminal, user equipment (UE), a wirelesscommunication device, a terminal, a wireless terminal, and/or otherappropriate terminology.

FIG. 2 is a block diagram of a multiple-input multiple-output (MIMO)wireless communication system 200 that facilitates transmission anddetection of spatial data streams in accordance with various aspectsdescribed herein. In one example, system 200 includes an access point(AP) 210 that can communicate with an access terminal (AT) 220. Whileonly one AP 210 and AT 220 are illustrated in system 200 for brevity, itshould be appreciated that system 200 can include any number of APsand/or ATs. Further, while the following discussion generally relates tocommunication from the AP 210 to the AT 220 (e.g., communication overforward links 120 and 126), it should be appreciated that similarcomponents and techniques could be employed by the AP 210 and/or the AT220 for communication from the AT 220 to the AP 210 (e.g., communicationover reverse links 118 and 124).

In one example, AP 210 includes a data source 212 that can generate orotherwise obtain data for transmission to one or more ATs 220. Data fromdata source 212 can be sent to an encoding component 214 to process thedata for communication to AT 220 via MIMO transmission. At encodingcomponent 214, a series of bits comprising data to be transmitted to AT220 can be grouped into spatial streams for simultaneous transmission bytransmitters (TMTRs) 216 via antennas 218. Further, the encodingcomponent can modulate each spatial stream using one or more digitalmodulation techniques, such as phase-shift keying (PSK), binaryphase-shift keying (BPSK), quadrature phase-shift keying (QPSK),16-point quadrature amplitude modulation (16-QAM), 64-point quadratureamplitude modulation (64-QAM), and/or another suitable modulationtechnique, under which bits of data comprising each stream can be mappedto a series of modulation symbols based on a set of constellationpoints. Additionally and/or alternatively, orthogonal frequency divisionmultiplexing (OFDM) can be utilized to divide a spatial stream amongmultiple orthogonal subcarriers such that each subcarrier can beindividually modulated using one or more modulation techniques. Mappedmodulation symbols for each stream can then be provided to respectivetransmitters 216 for communication to AT 220 as modulated analog signalsvia a series of N_(T) antennas 218.

At an AT 220, spatial streams corresponding to signals transmitted bythe AP 210 can be received by a series of N_(R) receivers (RCVRs) 224via respective antennas 222. In one example, an N_(R)-dimensionalreceive vector y corresponding to the streams received at an AT 220 canbe expressed as follows:y=Hx+n,  (1)where H is an NR×NT matrix that represents the effective MIMO channelthrough which transmitted signals pass between an AP 210 and an AT 220,x is an NT-dimensional transmit vector corresponding to the streamstransmitted from an AP 210, and n is an NR-dimensional vector thatrepresents additive noise.

In another example, spatial streams received by receivers 224 can beconveyed to a signal detection component 226, which can utilize thestreams received by the receivers 224 and knowledge of the effectiveMIMO channel to obtain the streams transmitted by the AP 210. Inaccordance with one aspect, signal detection component 226 can determinehard-decision outputs for bits in spatial streams received from the AP210 by determining the expected sign of each bit. For example, bitshaving a value of 1 can be represented by a hard-decision output of +1while bits having a value of 0 can be represented by a hard-decisionoutput of −1. Alternatively, signal detection component 226 candetermine soft-decision outputs for bits in spatial streams receivedfrom the AP 210 by determining the expected sign of each bit in additionto the likelihood that the respective expected sign for each bit hasbeen detected correctly, e.g., the likelihood that a bit was sent as +1or −1. In accordance with another aspect, the signal detection component226 can provide low-complexity soft-output detection by employing one ormore near-Soft-Output Maximum Likelihood Detection (near-SOMLD)algorithms as described infra. After successful detection, the detectedtransmitted streams can be provided to a data sink 228 for use by the AT220.

FIG. 3 is a block diagram illustrating an example signal detectioncomponent 300 that can be utilized in a MIMO communication system inaccordance with various aspects. By way of specific, non-limitingexample, signal detection component 300 can be used in MIMO systemsemploying IEEE 802.11n or a similar standard, Multi-User Detectionapplications, multi-mode fiber applications, and/or any other suitablecommunication systems or applications. Further, it should be appreciatedthat signal detection component 300 can be utilized by any appropriatenetwork entity in a MIMO communication system, such as an access point(e.g., an AP 210), an access terminal (e.g., an AT 220), and/or anyother suitable entity. In addition, a signal detection component 300 maybe internal to an associated network entity or an external componentthat is communicatively connected to one or more associated networkentities.

In accordance with one aspect, signal detection component 300 includes aMIMO channel processing component 310 that can determine and/or storeinformation relating to an effective MIMO channel through which spatialstreams are transmitted to a network entity (e.g., an AP 210 and/or anAT 220). In one example, a MIMO channel processing component 310 canrepresent channel information as a MIMO channel matrix, which can besimilar in structure to MIMO channel matrix H utilized in Equation (1).By way of specific example, MIMO channel processing component 310 canobtain the MIMO channel matrix through training based on, for example,preambles attached to one or more packets received at signal detectioncomponent 300; through one or more blind and/or semi-blind channelestimation techniques; and/or through other suitable techniques.

In a specific example, MIMO channel processing component 310 can performdecomposition and/or other appropriate pre-processing techniques on aMIMO channel matrix prior to signal detection. It should be appreciated,however, that pre-processing need not be performed by the MIMO channelprocessing component 310 and that signal detection component 300 canperform signal detection using one or more techniques described infrawith or without pre-processing by the MIMO channel processing component310. By way of additional specific, non-limiting example, MIMO channelprocessing component 310 can pre-process a MIMO channel matrix byperforming QR decomposition on the matrix. By utilizing QRdecomposition, MIMO channel processing component 310 can represent aMIMO channel matrix H as a product of an orthogonal matrix Q and anupper triangular matrix R. After performing QR decomposition, the MIMOchannel processing component 310 can communicate the decomposed channelmatrix QR to one or more appropriate components either in place of or inaddition to an unprocessed channel matrix H. In an additional example,MIMO channel processing component 310 can monitor for changes to theeffective MIMO channel and can adjust the channel matrix accordingly.

In accordance with another aspect, signal detection component 300includes a distance calculation component 320. Distance calculationcomponent 320 can obtain a series of received streams, which can becommunicated by an array of receivers (e.g., receivers 224) and/or othersuitable components or network entities. Alternatively, distancecalculation component 320 and/or other sub-components in signaldetection component 300 can receive soft-decision input valuescorresponding to a series of received streams, based on which signaldetection component 300 can perform near-soft-output maximum aposteriori probability (MAP) detection based on one or more of thesignal detection algorithms described infra.

In one example, distance calculation component 320 receives a series ofspatial streams corresponding to a receive vector y as utilized inEquation (1). Based on the receive vector y and a MIMO channel matrix Hreceived from MIMO channel processing component 310, distancecalculation component 320 can determine distances between transmittedstreams in a transmit vector x and all possible constellation pointcombinations used to modulate those streams (e.g., by an encodingcomponent 214). These determined distances can then be used by asoft-decision output generator 340 to determine soft-decision outputsreflecting expected values of bits in the transmitted streams as well astheir respective likelihoods. In accordance with one aspect,soft-decision outputs generated by soft-decision output generator 340that correspond to detected streams can then be utilized by a decoder(not shown) that can utilize an “outer code” to further process thestreams. An outer code utilized by the decoder can have error correctiveability that can, for example, introduce redundancy to improve thequality of wireless communication links to and/or from an entityemploying signal detection component 300. Further, an outer codeutilized by the decoder can be a convolutional code, a low-densityparity check (LDPC) code, and/or another appropriate type of code.

In another example, distance calculation component 320 can employ one ormore near-Soft-Output Maximum Likelihood Detection (near-SOMLD)algorithms by looping over a set of constellation points used tomodulate transmitted streams to determine distances between thetransmitted streams and the constellation points. These distances can bedetermined, for example, by using a distance metric such as theapproximated l¹-norm, the l¹-norm, the l²-norm, the l^(∞)-norm, and/oranother suitable distance metric. In conventional hard-decision MLD,calculating an optimal distance metric for each stream requires loopingover all possible constellation points for all streams. Thus, in thespecific example of N_(T) transmitted streams respectively modulatedusing a constellation of size M, conventional MLD requires distancecalculation for M^(N) ^(T) possible constellation point combinations. Asa result, conventional MLD has exponential computational complexity andis prohibitively complex for many applications. QR decomposition can beapplied to conventional MLD to allow the final dimension of the requiredcalculations to be obtained through slicing. However, such an algorithmretains exponential complexity as, for example, M^(N) ^(T) ⁻¹calculations are required where a constellation of size M is utilized tomodulate N_(T) transmitted streams. Similarly, QR-decomposed SOMLDrequires looping over all N_(T) transmitted streams such that eachstream can be represented as the final dimension and found throughslicing, resulting in a complexity order of N_(T)M^(N) ^(T) ⁻¹. Incontrast, distance calculation component 320 can calculate distancemetrics for transmitted streams over constellation points by utilizingtechniques for estimating values used for calculation via one or moresub-optimal MIMO algorithms such as Per-Stream List Detection (PSLD),Lattice-Reduced Detection (LRD), the Guided-M algorithm, and/or otherappropriate algorithms, such that looping over all possibleconstellation points is not required. As a result, distance calculationcomponent 320 can significantly lower required complexity forsoft-output detection while still providing close to optimal distancemetrics. In an additional example, distance calculation component 320can interact with a distance storage component 330 that can storecalculated distance metrics to further improve distance calculation andusage by signal detection component 300. By way of specific example,distance storage component 330 can be used to provide Enhanced MetricUsage (EMU) as described infra.

In accordance with a further aspect, signal detection component 300 caninclude a soft-decision output generator 340 that can utilize distancemetrics found for a series of transmitted streams to generatesoft-decision outputs relating to the expected values and likelihoods ofindividual bits in the transmitted streams. In one example, thesoft-decision output generator 340 can receive distance metrics relativeto a set of constellation points for a stream x_(p) in a transmit vectorx from distance calculation component 320 and/or distance storagecomponent 330. Based on these distance metrics, a soft-decision outputvalue can be derived per bit that represents x_(p) by, for example,using a Log-Likelihood Ratio (LLR). In one example, soft-decision outputgenerator 340 can calculate an approximation of the LLR for a kth bitb_(k) that represents x_(p) as follows:

$\begin{matrix}{{{L( b_{k} )} = {\frac{1}{\sigma_{n}^{2}}( {{\min\limits_{{x_{p}❘b_{k}} = 0}{d( x_{p} )}} - {\min\limits_{{x_{p}❘b_{k}} = 1}{d( x_{p} )}}} )}},} & (2)\end{matrix}$where d(x_(p)) is a distance metric received from the distancecalculation component 320 and/or distance storage component 330 as afunction of x_(p), the minima are searched over all values (e.g., allpossible constellation points) of x_(p) for which b_(k)=0 and b_(k)=1,respectively, and σ_(n) ² denotes the noise variance of additive noise nas utilized in Equation (1). Alternatively, it should be appreciatedthat the soft-decision output generator can utilize any other suitablesoft-decision technique either in addition to or in place of the LLRcalculation. Further, soft-decision outputs can further be quantizedinto a predetermined number of bits after calculation thereof. After thesoft-decision outputs are generated, they can be provided as detectedstream output from the signal detection component 300. Additionallyand/or alternatively, the soft-decision output generator 340 can providehard-decision outputs per bit in the transmitted streams by, forexample, determining the sign of respective soft-decision outputs.

Referring to FIGS. 4-8, methodologies for signal detection in a wirelesscommunication network are illustrated. While, for purposes of simplicityof explanation, the methodologies are shown and described as a series ofacts, it is to be understood and appreciated that the methodologies arenot limited by the order of acts, as some acts may, in accordance withone or more embodiments, occur in different orders and/or concurrentlywith other acts from that shown and described herein. For example, thoseskilled in the art will understand and appreciate that a methodologycould alternatively be represented as a series of interrelated states orevents, such as in a state diagram. Moreover, not all illustrated actsmay be required to implement a methodology in accordance with one ormore embodiments.

With reference to FIG. 4, illustrated is a methodology 400 forlow-complexity near-soft-output maximum likelihood detection(near-SOMLD) in a MIMO communication system (e.g., a communicationsystem 200). It is to be appreciated that methodology 400 can beperformed by a base station (e.g., an AP 210), a mobile terminal (e.g.,an AT 220), and/or any other suitable entity in a wireless communicationnetwork. Methodology 400 begins at block 402, wherein pre-processing isperformed on a channel matrix (e.g., by a MIMO channel processingcomponent 310 at a signal detection component 300) that represents theeffective MIMO channel between a transmitting entity and a receivingentity in the MIMO system. By way of specific, non-limiting example,pre-processing performed at block 402 can include QR decomposition,wherein a channel matrix H is decomposed into a product QR of a unitaryor orthonormal matrix Q and an upper triangular matrix R. Alternatively,matrix Q can be an orthogonal matrix. It should be appreciated, however,that QR decomposition is only one example of pre-processing that can beperformed at block 402 and other pre-processing and/or matrixdecomposition techniques can be performed in addition to or in place ofQR decomposition. Further, it should be appreciated that thepre-processing at block 402 is optional and need not be performed inmethodology 400. After the optional pre-processing at block 402,methodology 400 is initialized for a first transmitted stream at block404. Methodology 400 can then proceed for respective transmitted streamsto be detected as illustrated by blocks 406-410. In one example, thetransmitted streams utilized at blocks 406-410 can be represented by atransmit vector x as used in Equation (1).

In one example, methodology 400 can proceed for each transmitted streamto be detected at blocks 406-410 as follows. At block 406, each streamis looped over a set of constellation points (e.g., by a distancecalculation component 320 at a signal detection component 300) toestimate other elements using a sub-optimal MIMO algorithm. Elementsestimated at block 406 can be, for example, other transmitted streamsand/or any other elements necessary to compute distance metrics at block408. In addition, the set of constellation points can represent a set ofmodulation symbols used by an entity in the MIMO system that transmittedthe streams to be detected by methodology 400. As generally describedsupra, by estimating the other elements for each stream at block 406 forthe set of constellation points, it is not necessary to loop over allpossible combinations of constellation points for each transmittedstream as is required in conventional SOMLD algorithms. As a result,signal detection complexity can be greatly reduced while still allowingthe calculation of close to optimal distance metrics and soft outputs.By way of specific, non-limiting example, sub-optimal MIMO algorithmsthat can be used at block 406 include Per-Stream List Detection (PSLD),Lattice-Reduced Detection (LRD), a Guided-M algorithm, Zero Forcing(ZF), a Minimum Mean Square Error (MMSE) algorithm, and/or anothersuitable algorithm. Example algorithms are detailed in the followingdrawings and related description.

After looping completes for each stream at block 406, methodology 400proceeds to block 408, wherein distance metrics for the current streamare determined over the constellation points looped over in block 406(e.g., by a distance calculation component 320 at a signal detectioncomponent 300). In one example, the distance metrics are obtained byusing a channel matrix representing the effective MIMO channel overwhich the transmitted streams were received, which may or may not bepre-processed at block 402. Additionally, distance metrics at block 408can be determined by using a distance metric such as the approximatedl¹-norm, the l¹-norm, the l²-norm, the l^(∞)-norm, and/or anothersuitable distance metric.

After the distance metrics for the current stream are determined atblock 408, methodology 400 then proceeds to block 410 to determinewhether further transmitted streams are present. If further streams arepresent, methodology 400 advances to the next transmitted stream atblock 412 and repeats blocks 406-410 for said stream. If no furthertransmitted streams are present, methodology 400 concludes at block 414by obtaining soft-decision outputs based on the distance metricsdetermined at block 408 for each stream (e.g., via a soft-decisionoutput generator 340 at a signal detection component 300). By way ofspecific, non-limiting example, soft-decision outputs can be generatedat 414 by determining Log-Likelihood Ratios (LLRs) for each bit in thetransmitted streams based on the distance metrics calculated at block408. It should be appreciated, however, that other techniques forsoft-output generation could be utilized at block 414. In addition, itshould be appreciated that hard-decision outputs can also be generatedat block 414 by, for example, determining the sign of respectivesoft-decision outputs. In another example, hard-decision outputs for atransmitted stream can be generated by performing reverse constellationmapping for a constellation point that minimizes a distance metriccalculated at block 408 for the transmitted stream. Accordingly, ahard-decision output for a transmitted stream x₃ can be determined bysearching for a minimum distance metric d(x₃) calculated at block 408and its corresponding value x₃. Based on the determined x₃ value, thereverse of the constellation mapping can be used to obtain the bits ofthe determined x₃ value and the values estimated for its correspondingx₂ and x₁ at block 406.

FIG. 5 illustrates a methodology 500 for near-SOMLD in a MIMOcommunication system using a Per-Stream List Detection (PSLD) algorithm.Methodology 500 can be performed by a base station, a mobile terminal,and/or any other suitable entity in a wireless communication network. Inthe following description, PSLD is generally described for a series of 3transmitted streams (e.g., from 3 transmit antennas 218 at an AP 210).It should be appreciated, however, that methodology 500 can be similarlyapplied for any number of transmitted streams. Further, the followingdescription relates to a specific, non-limiting example of PSLD whereinthe approximated l¹-norm is used as distance metric as follows:

$\begin{matrix}{d = {{{\text{Re}( {y_{1} - {\begin{pmatrix}h_{11} & h_{12} & h_{13}\end{pmatrix}x}} )}} + {{{Im}( {y_{1} - {\begin{pmatrix}h_{11} & h_{12} & h_{13}\end{pmatrix}x}} )}} + \ldots + {{\text{Re}( {y_{N_{r}} - {\begin{pmatrix}h_{N_{r}1} & h_{N_{r}2} & h_{N_{r}3}\end{pmatrix}x}} )}} + {{{\text{Im}( {y_{N_{r}} - {\begin{pmatrix}h_{N_{r}1} & h_{N_{r}2} & h_{N_{r}3}\end{pmatrix}x}} )}}.}}} & (3)\end{matrix}$However, it should be appreciated that other norms can also be used forthe distance metric.

Methodology 500 can begin at block 502, wherein QR decomposition isperformed on a channel matrix representing the effective MIMO channel togenerate a QR orientation for each transmitted stream. In one example,QR decomposition can be performed at block 502 for three permutations ofa channel matrix H as used in Equation (1) such that every row of H ispermuted to be the last row only once. QR decomposition can then beperformed on each permutation to obtain three QR “orientations.” Whilethe discussion of the following blocks in FIG. 5 generally relates tocalculating soft-decision outputs based on QR orientations for eachtransmitted stream, it should be appreciated that QR decomposition atblock 502 is optional and need not be performed as part of methodology500 and that methodology 500 can be performed for a non-decomposedchannel matrix in a similar manner to the following description.

Methodology 500 next proceeds to block 504, wherein looping over a setof constellation points is performed for each transmitted stream inorder to estimate other elements needed for distance calculation using asub-optimal MIMO algorithm based on PSLD. By way of specific,non-limiting example, estimation can be performed by utilizing zeroforcing (ZF), ZF with Successive Interference Calculation, Minimum MeanSquare Error (MMSE) estimation, and/or other suitable sub-optimal MIMOalgorithms. While the following relates to the specific example of ZFwith Successive Interference Cancellation, it is to be appreciated thatany sub-optimal MIMO algorithm could similarly be used at block 504, andit is further to be appreciated that all such algorithms are intended tofall within the scope of the hereto appended claims.

Per received MIMO vector y, three QR orientations as generated at block502 can be used to loop over all transmitted streams, herein denoted asx₃, x₂, and x₁, respectively. For brevity, the following descriptionrelates only to acts performed at block 504 for the first orientation,with H_(permuted)=H=QR, and only describes the loop over the set ofconstellation points for transmitted stream x₃. It should beappreciated, however, that the described acts at block 504 can besimilarly performed for other transmitted streams.

In one example, the estimation at block 504 for transmitted stream x₃can proceed as follows. Prior to looping over the constellation points,an intermediate vector y′ can be determined by using the equationy′=Q(1:N_(R),1:N_(T))^(H)y, where Q(1:N_(R), 1:N_(T)) represents the setof elements in Q having indices of 1 to N_(R) by 1 to N_(T). From theintermediate vector y′, the transmitted stream x₃ can be looped over theset of constellation points to determine a second intermediate vector y″for each possible value of x₃ by using the equation y″=y′−R(1:3,3)x₃.Based on the intermediate vectors y″ determined for each constellationpoint, corresponding transmitted streams x₂ can be estimated by usingthe equation x₂=Slice(y″₂/r₂₂), where Y″₂ is the second element of y″,Slice( ) is a slicing operation to the nearest constellation point, andr₂₂ is entry (2,2) of R. By finding x₂, an l¹-norm approximation ofy″₂−r₂₂x₂ that can be used at block 506, which is|Re(y″₂−r₂₂x₂)|+|Im(y″₂−r₂₂x₂)|, can then be determined. Based on this,a third intermediate value y′″₁ can be calculated using the equationy′″₁=y″₁−r₁₂x₂, and from this equation transmitted stream x₁ can beestimated using the equation x₁=Slice(y′″₁/r₁₁). From the estimatedvalue of x₁, an l¹-norm approximation of y′″₁−r₁₁x₁ that can be utilizedat block 506, which is |Re(y′″−r₁₁x₁)|+|Im(y′″−r₁₁x₁)|, can bedetermined.

After estimation is performed at block 504, methodology 500 can proceedto block 506, wherein distance metrics are determined for thetransmitted streams over the constellation points. While blocks 504 and506 are illustrated as two separate acts in methodology 500, it shouldbe appreciated that the acts described at blocks 504 and 506 can beexecuted together, e.g., distance metrics can be calculated at block 506after each constellation point looped over at block 504, oralternatively distance metrics at block 506 can be calculated for eachstream for which looping is performed at block 504. By way of specific,non-limiting example, distance metric calculation at block 506 can beperformed as follows. First, for a transmitted stream x₃, a distancemetric can be calculated for respective possible constellation pointsfor transmitted stream x₃ using the approximated l¹-norm given byEquation (3) as follows:

$\begin{matrix}{{d( x_{3} )} = {{{\text{Re}( {y_{1}^{\prime\prime\prime} - {r_{11}x}} )}} + {{\text{Im}( {y_{1}^{\prime\prime\prime} - {r_{11}x_{1}}} )}} + {{\text{Re}( {y_{2}^{\prime\prime} - {r_{22}x_{2}}} )}} + {{\text{Im}( {y_{2}^{\prime\prime} - {r_{22}x_{2}}} )}} + {{\text{Re}( y_{3}^{\prime\prime} )}} + {{\text{Im}( y_{3}^{\prime\prime} )}}}} & (4)\end{matrix}$Similar looping and distance metric calculation can then be performedfor transmitted streams x₂ and x₁ at blocks 504 and 506 to obtaindistance metrics for each possible constellation point in eachtransmitted stream.

After distance metrics for the transmitted streams are calculated atblock 506, methodology 500 can conclude at block 508 by obtainingsoft-decision outputs by calculating log-likelihood ratios (LLRs) foreach bit in the transmitted streams based at least in part on thedistance metrics determined at block 506. By way of specific example,LLRs can be determined for a kth bit b_(k) in a transmitted stream x₁using the LLR expression given by Equation (2) as follows:

$\begin{matrix}{{L( b_{k} )} = {\frac{1}{\sigma_{n}^{2}}{( {{\min\limits_{{x_{1}❘b_{k}} = 0}{d( x_{1} )}} - {\min\limits_{{x_{1}❘b_{k}} = 1}{d( x_{1} )}}} ).}}} & (5)\end{matrix}$Additionally, LLRs for the other transmitted streams in x can becomputed using similar LLR expressions to those given in Equations (2)and (5).

FIG. 6 illustrates a methodology 600 for near-SOMLD in a MIMOcommunication system using a Lattice-Reduced Detection (LRD) algorithm.Methodology 600 can be performed by a base station, a mobile terminal,and/or any other suitable entity in a wireless communication network. Inthe following description, LRD is generally described for a series of 3transmitted streams (e.g., from 3 transmit antennas 218 at an AP 210).It should be appreciated, however, that methodology 600 can be similarlyapplied for any number of transmitted streams.

Methodology 600 can begin at block 602, wherein QR decomposition isperformed on a channel matrix representing the effective MIMO channel togenerate a QR orientation for each transmitted stream. In one example,QR decomposition can be performed at block 602 for three permutations ofa channel matrix H as used in Equation (1) such that every row of H ispermuted to be the last row only once. QR decomposition can then beperformed on each permutation to obtain three QR “orientations.” Whilethe discussion of the following blocks in FIG. 6 generally relates tocalculating soft-decision outputs based on QR orientations for eachtransmitted stream, it should be appreciated that QR decomposition atblock 602 is optional and need not be performed as part of methodology600 and that methodology 600 can be performed for a non-decomposedchannel matrix in a similar manner to the following description.

Methodology 600 next proceeds to block 604, wherein scaling and/orshifting factors are applied to a receive vector to transform eachelement in the receive vector to a complex integer. This can beperformed, for example, to facilitate Lattice-Basis Reduction (LBR) atblock 606. In one example, the receive vector utilized at block 604 canbe a receive vector y as used in Equation (1), which can be obtainedfrom a set of receivers and/or other suitable components. In accordancewith one aspect, LRD performed in methodology 600 is based on LBR. UnderLBR, a matrix P is determined such that both P and P⁻¹ consist only ofcomplex integer entries and such that H′=HP, where H′ is another basis,is more orthogonal. Thus, a point y represented by x in the basis H canbe represented by z=P⁻¹x in the basis H′, and this can be expressed byusing the equation y=Hx=(HP)(P⁻¹x)=H′z. Further, if x is a vector havingcomplex integer constellation points, simple rounding in the “z-domain”can be used for element estimation at block 608 since P⁻¹ has complexinteger entries.

Accordingly, scaling and shifting can be performed on y at block 604 totransform the MIMO system model into complex integer representationsthat can be used for LBR and LRD. In one example, the vector y can bescaled and shifted as follows to obtain a scaled and shifted versiony_(s+s):y=Hx+ny _(s+s) =c _(scale) y+Hc _(shift)y _(s+s) =H(c _(scale) x+c _(shift))+c _(scale) n′y _(s+s) =Hs+n′  (6)where c_(scale)=0.5√{square root over (((M−1)/1.5))}, M is the size ofthe constellation used for transmission of the streams to be detected(e.g., the size of an M-QAM modulation scheme utilized by an encodingcomponent 214), and c_(shift) is an N_(T)-dimensional vector with allelements equal to −0.5−0.5j. In one specific example, x consists solelyof constellation points in a modulation scheme used for transmission,and as a result s is its complex integer representation.

From the above, it can be observed that the second line of Equation (6)can be applied at block 604 to transform a received vector into a formatsuitable for LBR to be performed at block 606. Further, it can beobserved that the transformation given by Equation (6) can result inbetter performance with sub-optimal MIMO detection techniques. Forexample, “simple” Zero-Forcing (ZF) MIMO detection is applied bymultiplying y_(s+s) by (HP)⁻¹ as follows:

$\begin{matrix}\begin{matrix}{{({HP})^{- 1}y_{s + s}} = {{({HP})^{- 1}{HPP}^{- 1}s} + n^{\prime}}} \\{= {{P^{- 1}s} + {({HP})^{- 1}{n^{\prime}.}}}}\end{matrix} & (7)\end{matrix}$Since HP is more orthogonal than H, and as a result (HP)⁻¹n′ does notcause as much noise enhancement as H⁻¹n in “plain” ZF, improvedperformance can be achieved by utilizing Equation (7). Furthermore,since P⁻¹s can be composed of complex integer values, slicing operationswith respect to z can be performed using simple rounding operations. Theestimates of z and s can then be found as follows:z _(est)=round(P ⁻¹ s+(HP)⁻¹ n′)s _(est) =Pz _(est)  (8)

As one of ordinary skill in the art can appreciate, it may be difficultto consider constellation boundaries with respect to z. As a result,estimated values for s or x may fall outside the constellationboundaries with respect to s or x. Accordingly, an extra slicing stepwould be needed for hard-decision output decoding to obtainconstellation points within the constellation boundaries. However, itshould be appreciated that the extra slicing step is not always requiredfor soft-decision output decoding, as it may be better for performanceand complexity to carry out detection with respect to s, for example, byusing the equation s_(est)=Pz_(est). Based on this, the Euclideandistance metric then becomes the following:

$\begin{matrix}\begin{matrix}{d^{2} = {{y - {Hx}_{est}}}^{2}} \\{\approx {\frac{1}{c_{scale}^{2}}{{y_{s + s} - {Hs}_{est}}}^{2}}} \\{= {\frac{1}{c_{scale}^{2}}{{y_{s + s} - {HPz}_{est}}}^{2}}}\end{matrix} & (9)\end{matrix}$

Once scaling and shifting is performed at block 604, methodology 600 canproceed to block 606, wherein looping over a set of constellation pointsis performed for each transmitted stream in order to estimate otherelements needed for distance calculation using a sub-optimal MIMOalgorithm based on MRD. In one example, looping is performed per spatialstream at block 606 over the possible constellation points of thatspatial stream and LBR is used to estimate the other two spatialstreams. While the following description relates to performing LBR on achannel matrix decomposed using QR decomposition, it should beappreciated that similar techniques can be utilized for performing LBRon a non-decomposed channel matrix or a channel matrix decomposed usinganother decomposition technique. Further, while the followingdescription generally relates to a series of three transmitted streams,it should be appreciated that similar techniques can be utilized todetect any number of transmitted streams.

In a specific example, a first QR orientation can be applied on thenormal order of H=[h₁ h₂ h₃], and looping can be performed at block 606for all possible values (e.g., all possible constellation points) oftransmitted stream x₃. Then for the first QR orientation, withH_(permuted)=H=QR, LBR can be performed on the first two rows of R toobtain a modified Q and R, which can be expressed as Q_(LR) and R_(LR),such that Q_(LR)(1:N_(r), 1:N_(t))R_(LR)(1:N_(t),1:N_(t))=H_(permuted)P′, where P′ has the following structure:

$\begin{matrix}{P^{\prime} = {\begin{pmatrix}p_{11} & p_{12} & 0 \\p_{21} & p_{22} & 0 \\0 & 0 & 1\end{pmatrix} = {\begin{pmatrix}P & 0_{2 \times 1} \\0_{1 \times 2} & 1\end{pmatrix}.}}} & (10)\end{matrix}$

Because looping is performed at block 606 for all values of x₃, itshould be appreciated that there is no need to affect the last column ofH_(permuted) by the LBR.

In another specific example, the LBR on R(1:N_(T)−1, 1:N_(T)) (e.g., onR(1:2, 1:3)) is detailed by the following pseudo code in Table 1.

TABLE 1 Pseudo code for LBR on R(1:N_(T)−1, 1:N_(T)). (initialization) k= 2 Q′_(LR) = Q(1:Nr,1:Nt−1) R′_(LR) = R(1:Nt−1,1:Nt)  (P is the twodimensional identity matrix) P = I_(Nt−1)  (actual LBR) while k <= Nt−1for ii = k−1:−1:1    mu = round(R′_(LR)(ii,k) / R′_(LR)(ii,ii))    if mu~= 0       R′_(LR)(1:ii,k) = R′_(LR)(1:ii,k) − mu * R′_(LR)(1:ii,ii)     P(:,k) = P(:,k) − mu * P(:,ii)     end    end    delta = 0.75    ifdelta * R′_(LR)(k−1,k−1){circumflex over ( )}2 >RT′_(LR)(k,k){circumflex over ( )}2 +    abs(R′_(LR)(k−1,k)) {circumflexover ( )}2    (swap columns of R′_(LR) and P)    r_temp = R′_(LR)(:,k)   R′_(LR)(:,k) = R′_(LR)(:,k−1)    R′_(LR)(:,k−1) = r_temp    p_temp =P(:,k)    P(:,k) = P(:,k−1)    P(:,k−1) = p_temp    (Make sure Rmaintains its upper triangular structure)    alpha =R′_(LR)(k−1,k−1)/norm(R′_(LR)(k−1:k,k−1))    beta =R′_(LR)(k,k−1)/norm(R′_(LR)(k−1:k,k−1))    G = [-alpha beta; -beta-conj(alpha)]    R′_(LR)(k−1:k,k−1:Nt) = G^(H) * R′_(LR)(k−1:k,k−1:Nt)   Q′_(LR)(:,k−1:k) = Q′_(LR)(:,k−1:k) * G    k = max(k−1,2)    else   k = k+1 end end Q_(LR)(1:Nr,1:Nt−1) = Q_(LR)′ R_(LR)(1:Nt−1,1:Nt) =R_(LR)′ (the 3rd column of Q_(LR) equals the 3rd column of Q)Q_(LR)(1:Nr,Nt) = Q(1:Nr,Nt) (the 3rd row of R_(LR) equals the 3rd rowof R) R_(LR)(Nt,1:Nt) = R(Nt,1:Nt)

As the pseudo code in Table 1 illustrates, a check is performed on thenumber of times, denoted by the variable mu, the target column of R canbe subtracted from the other columns. Next, it is determined whether thecolumn with the most power is the rightmost column (i.e., the(N_(T)−1)th column). If the column with the most power is not therightmost column, the rightmost column and the column with the mostpower are swapped. After swapping columns, a rotation matrix can then beapplied to maintain the upper triangular structure of R.

In one example, by using the LBR operation described above, loopingperformed at block 606 can proceed as follows. While the followingdescription relates to looping for a third transmitted stream x₃, itshould be appreciated that looping can be similarly performed at block606 for other transmitted streams. First, based on a scaled and shiftedreceived vector y_(s+s) obtained at block 604, which can be expressed asfollows:y _(s+s) =c _(scale) y+H _(permuted) c _(shift),  (11)an intermediate vector y′ can be determined by using the equationy′=Q_(LR)(1:N_(r),1:N_(t))^(H)y_(s+s). Based on the vector y′, thetransmitted stream x₃ can be looped over the set of possibleconstellation points to determine a second intermediate vector y″ foreach possible value of x₃ by using the equation y″=y′−R_(LR)(1:3,3)z₃,where R_(LR)(1:3,3) are the first three elements of the third column ofR_(LR) and z₃=c_(scale)x₃+c_(shift), where c_(shift) is one entry ofc_(shift). In one example, respective values of z₃ can be pre-calculatedprior to looping at block 606. Based on the intermediate vectors y″determined for each constellation point, a corresponding value for z₂can be estimated by using the equation z₂=round(y″²/r_(LR,22)), whereY″₂ is the second element of y″, round( ) is a rounding operation to thenearest complex integer, and r_(LR,22) is entry (2,2) of R_(LR). Byfinding z₂, the l¹-norm approximation of y″₂−r_(LR,22)z₂, which is|Re(y″₂−r_(LR,22)z₂)|+|Im(y″₂−r_(LR,22)z₂)|, can then be determined.Based on this, a third intermediate value y′″₁ can be calculated usingthe equation y′″₁=y″₁−r_(LR,12)z₂, and from this equation acorresponding value for z₁ can be estimated using the equationz₁=round(y′″₁/r_(LR,11)). From the estimated value of x₁, an l¹-normapproximation of y′″₁−r_(LR,11)z₁ that can be utilized at block 606,which is |Re(y′″₁−r_(LR,11)z₁)|+|Im(y′″₁−r_(LR,11)z₁)|, can bedetermined.

Based on these calculations, for transmitted stream x₃, a distancemetric can then be calculated for each possible value (e.g., eachpossible constellation point) for x₃ using the approximated l¹-normgiven by Equation (3) as follows:

$\begin{matrix}{{d( x_{3} )} = {{{\text{Re}( {y_{1}^{\prime\prime\prime} - {r_{{LR},11}z_{1}}} )}} + {{\text{Im}( {y_{1}^{\prime\prime\prime} - {r_{{LR},11}z_{1}}} )}} + {{\text{Re}( {y_{2}^{\prime\prime} - {r_{{Lr},22}z_{2}}} )}} + {{\text{Im}( {y_{2}^{\prime\prime} - {r_{{LR},22}z_{2}}} )}} + {{\text{Re}( y_{3}^{\prime\prime} )}} + {{\text{Im}( y_{3}^{\prime\prime} )}}}} & (12)\end{matrix}$Similar looping and distance metric calculation can then be performed atblock 606 to obtain distance metrics for each transmitted stream.

After distance metrics for the transmitted streams are calculated atblock 606, methodology 600 can conclude at block 608 by obtainingsoft-decision outputs by calculating log-likelihood ratios (LLRs) foreach bit in the transmitted streams based at least in part on thedistance metrics determined at block 606. By way of specific example,LLRs can be determined for a kth bit b_(k) in a transmitted stream x₁using the LLR expression given by Equation (2) as follows:

$\begin{matrix}{{L( b_{k} )} = {\frac{1}{\sigma_{n}^{2}}{( {{\min\limits_{{x_{1}❘b_{k}} = 0}{d( x_{1} )}} - {\min\limits_{{x_{1}❘b_{k}} = 1}{d( x_{1} )}}} ).}}} & (13)\end{matrix}$Additionally, LLRs for the other transmitted streams in x can becomputed using similar LLR expressions to those given in Equations (2)and (13).

With reference now to FIG. 7, a methodology 700 for near-SOMLD in a MIMOcommunication system using a Guided-M algorithm is illustrated.Methodology 700 can be performed, for example, by an access point, anaccess terminal, and/or any other suitable entity in a wirelesscommunication network. In the following description, methodology 700 isgenerally described for a series of 3 transmitted streams (e.g., from 3transmit antennas 218 at an AP 210). It should be appreciated, however,that methodology 700 can be similarly applied for any number oftransmitted streams.

Methodology 700 can begin at block 702, wherein QR decomposition isperformed on a channel matrix representing the effective MIMO channel togenerate a QR orientation for each transmitted stream. In one example,QR decomposition can be performed at block 702 for three permutations ofa channel matrix H as used in Equation (1) such that every row of H ispermuted to be the last row only once. QR decomposition can then beperformed on each permutation to obtain three QR “orientations.” Whilethe discussion of the following blocks in FIG. 7 generally relates tocalculating soft-decision outputs based on QR orientations for eachtransmitted stream, it should be appreciated that QR decomposition atblock 702 is optional and need not be performed as part of methodology700 and that methodology 700 can be performed for a non-decomposedchannel matrix in a similar manner to the following description.

Methodology 700 next proceeds to block 704, wherein looping over a setof constellation points is performed for each transmitted stream toobtain a predetermined number of candidate estimates for other elementsneeded for distance calculation using a sub-optimal MIMO Guided-Malgorithm. As can be appreciated by one of ordinary skill in the art,full 3×3 SOMLD has exponential computational complexity. For example,full 3×3 SOMLD for a 64-QAM constellation conventionally requires asearch over 64*64 possibilities. In other words, if an outer loop isperformed over all possibilities of x₃, an inner loop over allpossibilities of x₂ would need to be performed for all possibilities ofx₃, from which slicing can be performed to get x₁. In contrast, using aGuided-M algorithm at block 704, required complexity is reduced bysearching over only M points in the second dimension in a guided way.

By way of specific, non-limiting example, looping performed at block 704can proceed as follows. The following description generally relates to aGuided-M algorithm that can be performed on a channel matrix decomposedusing QR decomposition (e.g., at block 702), herein referred to as a QRGuided-M algorithm (QRGM). However, it should be appreciated that thelooping at block 704 can be similarly performed for a non-decomposedchannel matrix and/or a channel matrix decomposed using anotherdecomposition technique.

First, prior to looping over the constellation points, an intermediatevector y′ can be determined by using the equationy′=Q(1:N_(R),1:N_(T))^(H)y, where Q(1:N_(R),1:N_(T)) represents the setof elements in Q having indices of 1 to N_(R) by 1 to N_(T). From theintermediate vector y′, the transmitted stream x₃ can be looped over theset of constellation points to determine a second intermediate vector y″for each possible value of x₃ by using the equation y″=y′−R(1:3,3)x₃.Based on the intermediate vectors y″ determined for each constellationpoint, an initial candidate estimate for corresponding transmittedstream x₂ can be estimated by using the equationx_(2,est)=Slice(y″₂/r₂₂), where y″₂ is the second element of y″, Slice() is a slicing operation to the nearest constellation point, and r₂₂ isentry (2,2) of R. By finding x₂, an l¹-norm approximation of y″₂−r₂₂x₂,which is |Re(y″₂−r₂₂x₂)|+|Im(y″₂−r₂₂x₂)|, can then be determined.

Once the initial candidate estimate x_(2,est) is determined, partialdistance metrics of the four constellation points surrounding x_(2,est)can be determined. In one example, the partial distance metrics can bedetermined by assuming that the vector y′ is scaled such that x_(2,est)is on a grid that can be expressed as {−7, −5, −3, −1, 1, 3, 5,7}+j*{−7, −5, −3, −1, 1, 3, 5, 7}. Based on this representation, thefour surrounding points can be chosen as x_(2,est)+[2, 2j, −2, −2j ]. Inone example, an additional check is performed to ensure that thesurrounding points do not fall outside the constellation boundaries.After the surrounding points are obtained, their partial distancemetrics can be found by taking the intermediate value y″₂−r₂₂x_(2,est),adding −r₂₂[2, 2j, −2, −2j], and then determining the four respectivel¹-norm approximations.

A third intermediate value y′″₁ can be calculated for x_(2,est) and itsfour surrounding points by using the equation y′″₁=y″₁−r₁₂x₂ for eachpoint. From these equations, corresponding candidate estimates fortransmitted stream x₁ can be estimated using the equationx₁=Slice(y′″₁/r₁₁). From the estimates of x₁, an l¹-norm approximationof y′″₁−r₁₁x₁ for each estimate, which is|Re(y′″₁−r₁₁x₁)|+|Im(y′″₁−r₁₁x₁)|, can be determined. For each set ofcandidate estimates, intermediate distance metrics can then bedetermined using the following equation:

$\begin{matrix}{{d( {x_{2},x_{3}} )} = {{{\text{Re}( {y_{1}^{\prime\prime\prime} - {r_{11}x_{1}}} )}} + {{\text{Im}( {y_{1}^{\prime\prime\prime} - {r_{11}x_{1}}} )}} + {{\text{Re}( {y_{2}^{\prime\prime} - {r_{22}x_{2}}} )}} + {{\text{Im}( {y_{2}^{\prime\prime} - {r_{22}x_{2}}} )}} + {{\text{Re}( y_{3}^{\prime\prime} )}} + {{\text{Im}( y_{3}^{\prime\prime} )}}}} & (14)\end{matrix}$From the distance metrics calculated using Equation (14) correspondingto the five initial candidate estimates of x₂, the estimate with theminimum distance metric can then be taken as a new estimate, which canbe denoted as x_(2, new) _(—) _(est) and three new points surroundingthe new estimate can be considered. For example, if x_(2, new) _(—)_(est)=x_(2,est)+2, the new points can be determined by x_(2, new) _(—)_(est)+[2, 2j, −2j]. It should be observed that x_(2,new) _(—) _(est)−2is not used since it results in x_(2,est), which was already determinedto not provide the minimum distance metric. Further checking can then beperformed to ensure that the new points do not fall outside theconstellation boundaries. After selection and checking of the newpoints, corresponding estimates for x₁ and the distance metrics of thethree new points can be found in a similar manner to the abovedescription regarding the points surrounding x_(2,est). In the eventthat x_(2, new) _(—) _(est)=x_(2,est), block 704 can be terminated orfour other points around x_(2,est) from the set, such as [2+2j, −2+2j,−2−2j, 2−2j], can be considered. Once the distance metrics aredetermined, x_(2,new) _(—) _(est) can be updated to reflect the pointhaving the minimum of the distance metrics corresponding to the pointsx_(2,new) _(—) _(est) and its surrounding points. The above calculationscan then be reiterated for the new x_(2,new) _(—) _(est) and itssurrounding points.

In one example, block 704 continues until M candidate points for x₂ havebeen considered. Once this condition is satisfied, methodology 700 cancontinue to block 706, wherein the candidate values of x₂ and x₁ forwhich minimum distance metrics were determined are selected. Similarlooping and distance metric calculation can then be performed at block706 to obtain minimum distance metrics for each transmitted stream.Alternatively, the calculations at block 704 can be conducted byderiving a gradient and using the gradient to determine the candidatevalue of x₂ with the minimum distance. In such an example, to achievesimilar performance as QRGM with M=8, only 4 points for x₂ need to beevaluated at the expense of the extra complexity to calculate thegradient.

After selecting the minimum distance metrics at block 706, methodology700 concludes at block 708 by obtaining soft-decision outputs bycalculating log-likelihood ratios (LLRs) for each bit in the transmittedstreams based at least in part on the minimum distance metricsdetermined at block 706. By way of specific example, LLRs can bedetermined for a kth bit b_(k) in a transmitted stream x₁ using the LLRexpression given by Equation (2) as follows:

$\begin{matrix}{{L( b_{k} )} = {\frac{1}{\sigma_{n}^{2}}{( {{\min\limits_{{x_{1}❘b_{k}} = 0}{d( x_{1} )}} - {\min\limits_{{x_{1}❘b_{k}} = 1}{d( x_{1} )}}} ).}}} & (15)\end{matrix}$Additionally, LLRs for the other transmitted streams in x can becomputed using similar LLR expressions to those given in Equations (2)and (15).

FIG. 8 illustrates a methodology 800 for low-complexity soft-outputdetection in a MIMO communication system with Enhanced Metric Usage(EMU). Methodology 800 can be performed, for example, by an accesspoint, an access terminal, and/or any other suitable entity in awireless communication network. In the following description,methodology 800 is generally described for a series of 3 transmittedstreams (e.g., from 3 transmit antennas 218 at an AP 210). It should beappreciated, however, that methodology 800 can be similarly applied forany number of transmitted streams. The general idea behind EMU is tomake more effective use of calculated distance metrics. For example, itcan be observed that distance metrics found for a given x₃ actually alsoapply to the estimated x₁ and x₂ for that x₃. It can happen that thedistance metric for the corresponding x₂, when going through a loop forx₂, is not as good. This may occur, for example, when column 2 of thechannel matrix H through which x₂ is received suffers from fading. Thus,by reusing the distance metrics derived in the x₃ loop for x₂ valuesestimated in the x₃ loop, a kind of distance metric diversity order canbe achieved.

The following description generally relates to EMU used with PSLD (e.g.,a PSLD algorithm implemented by methodology 500). However, it should beappreciated that EMU can also be used with any other suitable near-SOMLDalgorithm. Methodology 800 begins at block 802, wherein initial distancemetrics are stored for a set of constellation points in respectivearrays for a series of transmitted streams. In one example, for eachreceived MIMO vector y, distance metric storage arrays can beinitialized by setting distance metric storage arrays d_(store)(x₁),d_(store)(x₂), and d_(store)(x₃) to a high value, such as apredetermined value MaxVal, for all x₁, x₂, and x₃, respectively.

Methodology 800 can then be initialized for a first transmitted streamat block 804, after which looping can be performed at blocks 806-810. Atblock 806, looping can be performed for a currently considered streamover a set of constellation points to estimate other elements needed fordistance calculation and to determine distance metrics for therespective estimated elements. By way of specific, non-limiting example,looping for a transmitted stream x₃ can be performed at block 806 asfollows.

Prior to looping over the constellation points, an intermediate vectory′ can be determined by using the equation y′=Q(1:N_(R),1:N_(T))^(H)y.From the intermediate vector y′, the transmitted stream x₃ can be loopedover the set of constellation points to determine a second intermediatevector y″ for each possible value of x₃ by using the equationy″=y′−R(1:3,3)x₃. Based on the intermediate vectors y″ determined foreach constellation point, corresponding transmitted streams x₂ can beestimated by using the equation x₂=SliceAndIndex(y″₂/r₂₂), where y″₂ isthe second element of y″, SliceAndIndex( ) is a slicing operation to thenearest constellation point that also returns the index of theconstellation point for use at block 808, and r₂₂ is entry (2,2) of R.By finding x₂, an l¹-norm approximation of y″₂−r₂₂x₂, which is|Re(y″₂−r₂₂x₂)|+|Im(y″₂−r₂₂x₂)|, can then be determined. Based on this,a third intermediate value y′″₁ can be calculated using the equationy′″₁=y″₁−r₁₂x₂, and from this equation transmitted stream x₁ can beestimated using the equation x₁=SliceAndIndex(y′″₁/r₁₁). From theestimated value of x₁, an l¹-norm approximation of y′″₁−r₁₁x₁ that canbe utilized at block 506, which is |Re(y′″₁−r₁₁x₁)|+|Im(y′″−r₁₁x₁)|, canbe determined. A distance metric can then be calculated for the possibleconstellation points for x₃ and their corresponding estimated values ofx₁ and x₂ using the approximated l¹-norm given by Equation (3) asfollows:

$\begin{matrix}{{d( {x_{1},x_{2},x_{3}} )} = {{{\text{Re}( {y_{1}^{\prime\prime\prime} - {r_{11}x_{1}}} )}} + {{\text{Im}( {y_{1}^{\prime\prime\prime} - {r_{11}x_{1}}} )}} + {{\text{Re}( {y_{2}^{\prime\prime} - {r_{22}x_{2}}} )}} + {{\text{Im}( {y_{2}^{\prime\prime} - {r_{22}x_{2}}} )}} + {{\text{Re}( y_{3}^{\prime\prime} )}} + {{\text{Im}( y_{3}^{\prime\prime} )}}}} & (16)\end{matrix}$

Once the distance metrics are determined at block 806, methodology 800can proceed to block 808, wherein distance metrics for respectiveconstellation points determined for the current stream and estimatedother elements are stored in place of higher stored distance metrics forthe current stream and estimated other elements. More particularly, fora given transmitted stream x₃ and corresponding estimated values for x₁and x₂, the stored distance metrics d_(store)( ) can be updated asfollows:d _(store)(x ₁)=min(d _(store)(x ₁),d(x ₁ ,x ₂ ,x ₃))d _(store)(x ₂)=min(d _(store)(x ₂),d(x ₁ ,x ₂ ,x ₃))d _(store)(x ₃)=min(d _(store)(x ₃),d(x ₁ ,x ₂ ,x ₃))  (17)

After the distance metrics for the current stream are determined atblock 808, methodology 800 then proceeds to block 810 to determinewhether further transmitted streams are present. If further streams arepresent, methodology 800 advances to the next transmitted stream atblock 812 and repeats blocks 806-810 for said stream. If no furthertransmitted streams are present, methodology 800 concludes at block 814by obtaining soft-decision outputs based at least in part on the storeddistance metrics. By way of specific, non-limiting example,soft-decision outputs can be generated at 814 by calculatinglog-likelihood ratios (LLRs) for each bit in the transmitted streams.For example, LLRs can be determined for a kth bit b_(k) in a transmittedstream x₁ using the LLR expression given by Equation (2) for the storeddistance metrics as follows:

$\begin{matrix}{{L( b_{k} )} = {\frac{1}{\sigma_{n}^{2}}{( {{\min\limits_{{x_{1}❘b_{k}} = 0}{d_{store}( x_{1} )}} - {\min\limits_{{x_{1}❘b_{k}} = 1}{d_{store}( x_{1} )}}} ).}}} & (18)\end{matrix}$

Alternatively, the minimum searches d_(store)(x₁)=min(d_(store)(x₁),d(x₁, x₂, x₃)), etc., performed at block 808 can be combined with theabove LLR calculation. In such an example, minimum searchesd_(store)(x₁)=min(d_(store)(x₁), d(x₁, x₂, x₃)), etc., are not performedat block 808, and instead each distance metric d(x₁, x₂, x₃) for eachrespective combination of spatial streams can be stored at block 808together with their corresponding x₁, x₂, and x₃. From this information,LLRs can then be calculated at block 814, as illustrated by thefollowing:

$\begin{matrix}{{L( b_{k} )} = {\frac{1}{\sigma_{n}^{2}}{( {{\min\limits_{{x_{1}❘b_{k}} = 0}{d( {x_{1},x_{2},x_{3}} )}} - {\min\limits_{{x_{1}❘b_{k}} = 1}{d( {x_{1},x_{2},x_{3}} )}}} ).}}} & (19)\end{matrix}$

Thus, in an example of a 64-QAM constellation with three spatialtransmit streams, 3*64=192 distance metrics can be searched over to finddistance metrics for which the kth bit of x₁ is 0, after which theminimum

$\begin{matrix}{\min\limits_{{x_{1}❘b_{k}} = 0}{d( {x_{1},x_{2},x_{3}} )}} & (20)\end{matrix}$can be determined, and so on.

The minimum can be found over a large number of distance metrics, forexample, by representing the minimum distance metrics as binary numbersand scanning each number from the Most Significant Bit (MSB) to theLeast Significant Bit (LSB)). If the bits at a currently scanned bitposition differ among the distance metrics, then distance metrics havinga bit value of “1” on the currently scanned bit position can be labeledand removed from consideration as the minimum. If the LSB is reached, asingle remaining candidate, or any one of the remaining candidates ifmultiple remaining candidates are present, can be utilized as theminimum distance metric. In another example, this minimum searchalgorithm can be applied at block 810 to the minimum searches requiredto calculate approximated LLRs as follows. First, for the minimum searchover all d(x₁,x₂,x₃) given that bit b_(k) of x₁ is 0, all distancemetrics for which bit b_(k) of x₁ is 1 can be labeled and removed fromconsideration in the minimum search. Likewise, for the minimum searchover all d(x₁,x₂,x₃) given that bit b_(k) of x₁ is 1, all distancemetrics for which bit b_(k) of x₁ is 0 can similarly be labeled andremoved from consideration in the minimum search.

Referring now to FIG. 9, a block diagram illustrating an examplewireless communication system 900 in which one or more embodimentsdescribed herein may function is provided. In one example, system 900 isa multiple-input multiple-output (MIMO) system that includes atransmitter system 910 and a receiver system 950. It should beappreciated, however, that transmitter system 910 and/or receiver system950 could also be applied to a multi-input single-output system wherein,for example, multiple transmit antennas (e.g., on a base station), maytransmit one or more symbol streams to a single antenna device (e.g., amobile station). Additionally, it should be appreciated that aspects oftransmitter system 910 and/or receiver system 950 described herein couldbe utilized in connection with a single output to single input antennasystem.

In accordance with one aspect, traffic data for a number of data streamsare provided at transmitter system 910 from a data source 912 to atransmit (TX) data processor 914. In one example, each data stream canthen be transmitted via a respective transmit antenna 924. Additionally,TX data processor 914 can format, code, and interleave traffic data foreach data stream based on a particular coding scheme selected for eachrespective data stream in order to provide coded data. In one example,the coded data for each data stream may then be multiplexed with pilotdata using OFDM techniques. The pilot data can be, for example, a knowndata pattern that is processed in a known manner. Further, the pilotdata may be used at receiver system 950 to estimate channel response.Back at transmitter system 910, the multiplexed pilot and coded data foreach data stream can be modulated (i.e., symbol mapped) based on aparticular modulation scheme (e.g., BPSK, QSPK, M-PSK, or M-QAM)selected for each respective data stream in order to provide modulationsymbols. In one example, data rate, coding, and modulation for each datastream may be determined by instructions performed on and/or provided byprocessor 930.

Next, modulation symbols for all data streams can be provided to a TXMIMO processor 920, which may further process the modulation symbols(e.g., for OFDM). TX MIMO processor 920 may then provides N_(T)modulation symbol streams to N_(T) transmitters (TMTR) 922 a through 922t. In one example, each transmitter 922 can receive and process arespective symbol stream to provide one or more analog signals. Eachtransmitter 922 may then further condition (e.g., amplify, filter, andupconvert) the analog signals to provide a modulated signal suitable fortransmission over a MIMO channel. Accordingly, N_(T) modulated signalsfrom transmitters 922 a through 922 t can then be transmitted from N_(T)antennas 924 a through 924 t, respectively.

In accordance with another aspect, the transmitted modulated signals canbe received at receiver system 950 by N_(R) antennas 952 a through 952r. The received signal from each antenna 952 can then be provided to arespective receiver (RCVR) 954. In one example, each receiver 954 cancondition (e.g., filter, amplify, and downconvert) a respective receivedsignal, digitize the conditioned signal to provide samples, and thenprocesses the samples to provide a corresponding “received” symbolstream. An RX MIMO/data processor 960 can then receive and process theN_(R) received symbol streams from N_(R) receivers 954 based on aparticular receiver processing technique to provide N_(T) “detected”symbol streams. In one example, each detected symbol stream can includesymbols that are estimates of the modulation symbols transmitted for thecorresponding data stream. RX MIMO/data processor 960 can then processeach symbol stream at least in part by demodulating, deinterleaving, anddecoding each detected symbol stream to recover traffic data for acorresponding data stream. After successful recovery, the stream can beprovided to a data sink 964. Thus, the processing by RX MIMO/dataprocessor 960 may be complementary to that performed by TX MIMOprocessor 920 and TX data processor 914 at transmitter system 910.

In another example, RX MIMO/data processor 960 may be limited in thenumber of subcarriers that it may simultaneously demodulate. Forexample, RX MIMO/data processor 960 may be limited to 512 subcarriers at5 MHz, 128 subcarriers at 1.25 MHz, or 256 subcarriers at 2.5 MHz. Inanother example, RX MIMO/data processor 960 may be limited to 128subcarriers at 40 MHz or 64 subcarriers at 20 MHz. Further, the channelresponse estimate generated by RX MIMO/data processor 960 may be used toperform space/time processing at the receiver, adjust power levels,change modulation rates or schemes, and/or other appropriate actions.Additionally, RX MIMO/data processor 960 may further estimate channelcharacteristics such as, for example, signal-to-noise-and-interferenceratios (SNRs) of the detected symbol streams. RX MIMO/data processor 960can then provide estimated channel characteristics to a processor 970.In one example, RX MIMO/data processor 960 and/or processor 970 canfurther derive an estimate of the “operating” SNR for the system.Processor 970 can then provide channel state information (CSI), whichmay comprise information regarding the communication link and/or thereceived data stream. This information may include, for example, theoperating SNR. The CSI can then be processed by a TX data processor 978(which can be coupled to a data source 976), modulated by a modulator980, conditioned by transmitters 954 a through 954 r, and transmittedback to transmitter system 910.

Back at transmitter system 910, the modulated signals from receiversystem 950 can then be received by antennas 924, conditioned byreceivers 922, demodulated by a demodulator 940, and processed by a RXdata processor 942 to recover the CSI reported by receiver system 950.After successful recovery, the stream can be provided to a data sink944. In one example, the reported CSI can then be provided to processor930 and used to determine data rates as well as coding and modulationschemes to be used for one or more data streams. The determined codingand modulation schemes can then be provided to transmitters 922 forquantization and/or use in later transmissions to receiver system 950.Additionally and/or alternatively, the reported CSI can be used byprocessor 930 to generate various controls for TX data processor 914 andTX MIMO processor 920.

In one example, processor 930 at transmitter system 910 and processor970 at receiver system 950 direct operation at their respective systems.Additionally, memory 932 at transmitter system 910 and memory 972 atreceiver system 950 can provide storage for program codes and data usedby processors 930 and 970, respectively. Further, at receiver system950, various processing techniques may be used to process the N_(R)received signals to detect the N_(T) transmitted symbol streams. In oneexample, these processing techniques can include one or more ofmethodologies 400, 500, 600, 700, 800, and/or any other appropriatetechnique for near-SOMLD. Additionally and/or alternatively, processingtechniques utilized by receiver system 950 can include spatial andspace-time receiver processing techniques, which may also be referred toas equalization techniques, and/or “successive nulling/equalization andinterference cancellation” receiver processing techniques, which mayalso be referred to as “successive interference cancellation” or“successive cancellation” receiver processing techniques.

FIG. 10 is a block diagram of a system 1000 that coordinates modulationand transmission of spatial data streams in accordance with variousaspects described herein. In one example, system 1000 includes a basestation or access point 1002. As illustrated, access point 1002 canreceive signal(s) from one or more access terminals 1004 via a receive(Rx) antenna 1006 and transmit to the one or more access terminals 1004via a transmit (Tx) antenna 1008.

Additionally, access point 1002 can comprise a receiver 1010 thatreceives information from receive antenna 1006. In one example, thereceiver 1010 can be operatively associated with a demodulator (Demod)1012 that demodulates received information. Demodulated symbols can thenbe analyzed by a processor 1014. Processor 1014 can be coupled to memory1016, which can store information related to code clusters, accessterminal assignments, lookup tables related thereto, unique scramblingsequences, and/or other suitable types of information. In one example,access point 1002 can employ demodulator 1012 and/or processor 1014 toperform methodologies 400, 500, 600, 700, 800, and/or other similar andappropriate methodologies. Access point 1002 can also include amodulator 1018 that can multiplex a signal for transmission by atransmitter 1020 through transmit antenna 1008 to one or more accessterminals 1004.

FIG. 11 is a block diagram of a system 1100 that coordinates receptionand detection of spatial data streams in accordance with various aspectsdescribed herein. In one example, system 1100 includes an accessterminal 1102. As illustrated, access terminal 1102 can receivesignal(s) from one or more access points 1104 and transmit to the one ormore access points 1104 via an antenna 1108. Additionally, accessterminal 1102 can comprise a receiver 1110 that receives informationfrom antenna 1108. In one example, receiver 1110 can be operativelyassociated with a demodulator (Demod) 1112 that demodulates receivedinformation. Demodulated symbols can then be analyzed by a processor1114. Processor 1114 can be coupled to memory 1116, which can store dataand/or program codes related to access terminal 1102. Additionally,access terminal 1102 can employ demodulator 1112 and/or processor 1114to perform methodologies 400, 500, 600, 700, 800, and/or other similarand appropriate methodologies. Access terminal 1102 can also include amodulator 1118 that can multiplex a signal for transmission by atransmitter 1120 through antenna 1108 to one or more access points 1104.

FIG. 12 illustrates an apparatus 1200 that provides near soft-outputmaximum likelihood detection. It is to be appreciated that apparatus1200 is represented as including functional blocks, which can befunctional blocks that represent functions implemented by a processor,software, or combination thereof (e.g., firmware). Apparatus 1200 can beimplemented in a base station (e.g., an AP 210) and/or a terminal (e.g.,an AT 220) and can include a module for looping over constellationpoints per spatial transmitted stream to estimate other elements using asub-optimal MIMO algorithm 1202. Further, apparatus 1200 can include amodule for determining distance metrics for the streams over theconstellation points 1204 and a module for obtaining soft-decisionoutputs for each bit in the transmitted streams based on the determineddistance metrics 1206.

FIG. 13 illustrates an apparatus 1300 that provides near soft-outputmaximum likelihood detection via MIMO channel matrix pre-processing andutilization of sub-optimal MIMO algorithms. It is to be appreciated thatapparatus 1300 is represented as including functional blocks, which canbe functional blocks that represent functions implemented by aprocessor, software, or combination thereof (e.g., firmware). Apparatus1300 can be implemented in a base station (e.g., an AP 210) and/or aterminal (e.g., an AT 220) and can include a module for performingpre-processing on a MIMO channel matrix using QR decomposition and/orother suitable pre-processing techniques 1302. Further, apparatus 1300can comprise a module for looping over constellation points per spatialtransmitted stream to estimate other elements using a sub-optimal MIMOalgorithm based on one or more of PSLD, LRD, and a Guided-M algorithm1304; a module for determining distance metrics for the streams over theconstellation points 1306; and a module for obtaining soft-decisionoutputs by calculating log-likelihood ratios for each bit in thetransmitted streams based at least in part on the determined distancemetrics 1308.

FIG. 14 illustrates an apparatus 1400 that provides near soft-outputmaximum likelihood detection with Enhanced Metric Usage. It is to beappreciated that apparatus 1400 is represented as including functionalblocks, which can be functional blocks that represent functionsimplemented by a processor, software, or combination thereof (e.g.,firmware). Apparatus 1400 can be implemented in a base station (e.g., anAP 210) and/or a terminal (e.g., an AT 220) and can include a module forstoring initial distance metric arrays for a set of constellation pointsper spatial transmitted stream 1402. Further, apparatus 1400 cancomprise a module for looping over constellation points per spatialstream to estimate other elements using a sub-optimal MIMO algorithm1404, a module for determining distance metrics for the streams andestimated other elements over the constellation points 1406, a modulefor storing distance metrics for spatial streams and estimated otherelements in place of respective higher stored distance metrics forcorresponding constellation points 1408, and a module for obtainingsoft-decision outputs for each bit in the transmitted streams based onthe stored distance metrics 1410.

It is to be understood that the embodiments described herein may beimplemented by hardware, software, firmware, middleware, microcode, orany combination thereof. When the systems and/or methods are implementedin software, firmware, middleware or microcode, program code or codesegments, they may be stored in a machine-readable medium, such as astorage component. A code segment may represent a procedure, a function,a subprogram, a program, a routine, a subroutine, a module, a softwarepackage, a class, or any combination of instructions, data structures,or program statements. A code segment may be coupled to another codesegment or a hardware circuit by passing and/or receiving information,data, arguments, parameters, or memory contents. Information, arguments,parameters, data, etc. may be passed, forwarded, or transmitted usingany suitable means including memory sharing, message passing, tokenpassing, network transmission, etc.

For a software implementation, the techniques described herein may beimplemented with modules (e.g., procedures, functions, and so on) thatperform the functions described herein. The software codes may be storedin memory units and executed by processors. The memory unit may beimplemented within the processor or external to the processor, in whichcase it can be communicatively coupled to the processor via variousmeans as is known in the art.

What has been described above includes examples of one or moreembodiments. It is, of course, not possible to describe everyconceivable combination of components or methodologies for purposes ofdescribing the aforementioned embodiments, but one of ordinary skill inthe art may recognize that many further combinations and permutations ofvarious embodiments are possible. Accordingly, the described embodimentsare intended to embrace all such alterations, modifications andvariations that fall within the spirit and scope of the appended claims.Furthermore, to the extent that the term “includes” is used in eitherthe detailed description or the claims, such term is intended to beinclusive in a manner similar to the term “comprising” as “comprising”is interpreted when employed as a transitional word in a claim.Furthermore, the term “or” as used in either the detailed description orthe claims is meant to be a “non-exclusive or.”

What is claimed is:
 1. A method for generating soft-decision outputvalues for a set of transmitted spatial streams in a multiple-inputmultiple-output (MIMO) communication system, comprising: looping, by aprocessor in a wireless communication apparatus, over the set oftransmitted spatial streams and for a respective transmitted spatialstream: determining a plurality of constellation points for therespective transmitted spatial stream to estimate values for theconstellation points of the other transmitted streams based at least inpart on a sub-optimal MIMO algorithm without looping over all possiblecombinations of the constellation points of the other transmittedstreams; determining a set of distance metrics as values of theplurality of constellation points for the respective transmitted spatialstream; and generating soft-decision outputs for the respectivetransmitted stream based at least in part on the set of distancemetrics.
 2. The method of claim 1, wherein the sub-optimal MIMOalgorithm is based at least on Per-Stream List Detection (PSLD).
 3. Themethod of claim 2, wherein the sub-optimal MIMO algorithm based at leaston PSLD includes zero forcing with successive interference calculation.4. The method of claim 1, wherein the determining the plurality ofconstellation points includes: applying at least one of a scaling factorand a shifting factor to a channel matrix that represents an effectiveMIMO channel through which the set of transmitted spatial streams arereceived to convert respective entries in the channel matrix to complexintegers; and wherein the sub-optimal MIMO algorithm is based at leaston Lattice-Reduced Detection (LRD).
 5. The method of claim 1, whereinthe determining the plurality of constellation points includes:obtaining a predetermined number of estimated candidate values for othertransmitted streams using a sub-optimal MIMO Guided-M algorithm; andselecting estimated candidate values for the respective othertransmitted streams that minimize respective distance metrics for therespective transmitted stream over the set of constellation points. 6.The method of claim 1, further comprising decomposing a channel matrixthat represents an effective MIMO channel through which the set oftransmitted spatial streams are received, wherein the determining theplurality of constellation points includes estimating values for othertransmitted streams using the decomposed channel matrix.
 7. The methodof claim 6, wherein the decomposing the channel matrix includesperforming QR decomposition on the channel matrix.
 8. The method ofclaim 1, further comprising: storing initial distance metrics for a setof constellation points for the set of transmitted streams; wherein thedetermining the set of distance metrics includes: determining distancemetrics as values of the plurality of constellation points forrespective sets of transmitted spatial streams and correspondingestimated values for other transmitted streams, storing distance metricsfor respective sets of transmitted spatial streams and correspondingestimated values for other transmitted streams in place of higher storeddistance metrics for the respective sets of transmitted spatial streamsand corresponding estimated values for other transmitted streams; andwherein the generating soft-decision outputs includes generatingsoft-decision outputs for the respective transmitted streams based atleast in part on the stored distance metrics.
 9. The method of claim 1,further comprising generating harddecision outputs for the respectivetransmitted stream based at least in part on the generated soft-decisionoutputs.
 10. The method of claim 1, further comprising: generatinghard-decision outputs for the respective transmitted stream by searchingfor a minimum distance metric for a transmitted stream in the respectivetransmitted streams; and obtaining hard-decision outputs for thetransmitted stream and corresponding estimates for other respectivetransmitted streams based at least in part on a reverse constellationmapping.
 11. The method of claim 1, wherein the set of distance metricscomprise soft-decision input values respectively representing estimatedvalues of the transmitted spatial stream.
 12. The method of claim 11,wherein the soft-decision input values are generated by a decoder usingan outer code.
 13. The method of claim 1, wherein the determining theset of distance metrics includes determining the set of distance metricsas values of the plurality of constellation points for the respectivetransmitted spatial stream using at least one of an approximatedl¹-norm, an l¹-norm, an l²-norm, and an l^(∞)-norm.
 14. The method ofclaim 1, wherein the generating soft-decision outputs for the respectivetransmitted stream includes calculating log-likelihood ratios forrespective bits in the transmitted streams based at least in part on theset of distance metrics.
 15. The method of claim 1, wherein therespective transmitted spatial stream is modulated using phase-shiftkeying (PSK).
 16. The method of claim 1, wherein the respectivetransmitted spatial stream is modulated using quadrature amplitudemodulation (QAM).
 17. The method of claim 1, wherein the set oftransmitted spatial streams are allocated among a plurality ofsubcarriers using orthogonal frequency division multiplexing (OFDM),wherein: the determining includes determining a plurality ofconstellation points for the respective transmitted spatial streamallocated to respective subcarriers, the determining the set of distancemetrics includes determining distance metrics for respective transmittedspatial stream allocated to respective subcarriers, and the generatingsoft-decision outputs includes generating soft-decision outputs forrespective transmitted stream allocated to respective subcarriers. 18.The method of claim 1, wherein the determining the plurality ofconstellation points includes determining based on one or more of zeroforcing and a minimum mean square error algorithm.
 19. The method ofclaim 1, wherein the determining the plurality of constellation pointsincludes determining the plurality of constellation points forrespective subsets of the set of transmitted spatial streams to estimatevalues for transmitted streams not in the respective subsets based onthe sub-optimal MIMO algorithm.
 20. A wireless communications apparatus,comprising: a memory that stores data relating to a set of receivedstreams and a matrix corresponding to a channel through which a set oftransmitted streams corresponding to the set of received streams werecommunicated; and a processor configured to loop over the set oftransmitted spatial streams and for a respective transmitted spatialstream, to determine one or more constellation points for the respectivetransmitted stream to determine estimated values for the constellationpoints of the other transmitted streams and corresponding distancemetrics using the matrix and a sub-optimal MIMO algorithm withoutlooping over all possible combinations of the constellation points ofthe other transmitted streams, and to generate soft-decision outputs forthe respective transmitted stream based at least in part on the distancemetrics, wherein the soft-decision outputs for the respectivetransmitted stream are generated as log-likelihood ratios of thedetermined distance metrics.
 21. The wireless communications apparatusof claim 20, wherein the processor is further configured to determineone or more constellation points for the respective transmitted streamto determine estimated values for other transmitted streams andcorresponding distance metrics using the matrix and the sub-optimal MIMOalgorithm based on Per-Stream List Detection (PSLD).
 22. The wirelesscommunications apparatus of claim 20, wherein the processor is furtherconfigured: to perform at least one of a scaling operation and ashifting operation on the matrix to convert the matrix to a complexinteger representation; and to determine estimated values for othertransmitted streams and corresponding distance metrics using the matrixand the sub-optimal MIMO algorithm based on Lattice-Reduced Detection(LRD).
 23. The wireless communications apparatus of claim 20, whereinthe processor is further configured: to determine one or moreconstellation points for the respective transmitted stream to obtain apredetermined number of estimated candidates for other transmittedstreams and corresponding distance metrics using the matrix and a MIMOGuided-M algorithm; and to select estimated candidates for therespective other transmitted streams having minimum correspondingdistance metrics for the respective transmitted stream over the set ofconstellation points.
 24. The wireless communications apparatus of claim20, wherein the processor is further configured: to process the matrixusing a matrix decomposition technique; and to determine estimatedvalues for other transmitted streams and corresponding distance metricsusing the processed matrix and the sub-optimal MIMO algorithm.
 25. Thewireless communications apparatus of claim 24, wherein the processor isfurther configured to process the matrix using QR decomposition.
 26. Thewireless communications apparatus of claim 20, wherein: the memoryfurther stores data relating to respective arrays for storage ofdistance metrics for the set of transmitted streams over the one or moreconstellation points; and the processor is further configured: to storeinitial distance metrics for the set of transmitted streams over the oneor more constellation points in the respective arrays; to determineestimated values for other transmitted streams and correspondingdistance metrics; to store corresponding distance metrics in therespective arrays for sets of respective transmitted streams andestimated values for the other transmitted streams in place of highercorresponding stored distance metrics in the respective arrays; and togenerate soft-decision outputs for the respective transmitted streams aslog-likelihood ratios of the stored distance metrics.
 27. The wirelesscommunications apparatus of claim 20, wherein the processor is furtherconfigured to generate hard-decision outputs for the respectivetransmitted streams based on the determined distance metrics.
 28. Thewireless communications apparatus of claim 20, wherein the memoryfurther stores data relating to soft-decision input values for the setof received streams.
 29. The wireless communications apparatus of claim20, wherein the processor is further configured to determine distancemetrics using at least one of an approximated l¹-norm, an l¹-norm, anl²-norm, and an l^(∞)-norm.
 30. The wireless communications apparatus ofclaim 20, wherein the received streams are modulated using one or moreof PSK and QAM.
 31. The wireless communications apparatus of claim 20,wherein: the memory further stores data relating to respective frequencysubcarriers having received streams allocated thereto based on OFDM; andthe processor is further configured to generate soft-decision outputsfor the respective transmitted stream for the respective frequencysubcarriers.
 32. A system that facilitates multi-user detection in awireless communication system comprising the wireless communicationsapparatus of claim
 20. 33. A communication system apparatus thatprovides low-complexity near-soft-output maximum likelihood detectionfor a series of transmitted streams, comprising: means for looping overa set of transmitted spatial streams and for a respective transmittedspatial stream using: means for determining a set of constellationpoints for the respective transmitted stream to estimate values for theconstellation points of other transmitted streams using a suboptimalMIMO algorithm without looping over all possible combinations of theconstellation points of the other transmitted streams; means fordetermining distance metrics for the respective transmitted stream overthe set of constellation points; and means for obtaining soft-decisionoutputs for respective bits in the transmitted stream based on thedetermined distance metrics.
 34. The communication system apparatus ofclaim 33, wherein the sub-optimal MIMO algorithm is based at least onPer-Stream List Detection (PSLD).
 35. The communication system apparatusof claim 33, wherein the means for determining the set of constellationpoints includes: means for scaling and shifting a channel matrix toconvert respective entries in the channel matrix to complex integers;and means for estimating the other values using the channel matrix andthe sub-optimal MIMO algorithm based on Lattice-Reduced Detection (LRD).36. The communication system apparatus of claim 33, wherein the meansfor determining the set of constellation points includes: means fordetermining the set of constellation points for respective transmittedstreams to generate estimated candidate values for the other valuesusing a sub-optimal MIMO Guided-M algorithm; and means for selectingrespective estimated candidate values for the other values that minimizerespective distance metrics for the transmitted streams over the set ofconstellation points.
 37. The communication system apparatus of claim33, further comprising means for processing a channel matrix based atleast in part on QR decomposition, wherein the means for determining theset of constellation points includes means for estimating other valuesusing the channel matrix and the sub-optimal MIMO algorithm.
 38. Thecommunication system apparatus of claim 33, further comprising: meansfor storing initial distance metrics for the set of constellation pointsthat respectively correspond to the series of transmitted streams; andwherein the means for determining distance metrics includes: means fordetermining distance metrics for the respective transmitted stream andrespective estimated other values over the set of constellation points,and means for storing distance metrics for respective sets oftransmitted spatial streams and estimated other values in place ofcorresponding higher stored distance metrics; and wherein the means forobtaining soft-decision outputs includes means for obtainingsoft-decision outputs for respective bits in the transmitted streamsbased on the stored distance metrics.
 39. The communication systemapparatus of claim 33, wherein the means for obtaining soft-decisionoutputs includes means for calculating log-likelihood ratios forrespective bits in the transmitted streams based at least in part on thedetermined distance metrics.
 40. The communication system apparatus ofclaim 33, wherein the means for determining includes means forestimating other values using one or more of zero forcing, zero forcingwith successive interference cancellation, and a minimum mean squareerror algorithm.
 41. The communication system apparatus of claim 33,wherein the means for determining includes means for estimatingtransmitted streams that are not in the respective subsets using thesub-optimal MIMO algorithm.
 42. A multiple-input multiple-outputwireless communication system comprising the apparatus of claim
 33. 43.A multi-mode fiber-optic communication system comprising the apparatusof claim
 33. 44. A non-transitory computer-readable medium having storedthereon computer-executable instructions for soft value generation for aset of transmitted streams in a wireless communication system, theinstructions comprising: code for looping over the set of transmittedspatial streams and for a respective transmitted spatial streamexecuting: code for utilizing a channel matrix and a sub-optimal MIMOalgorithm to iteratively-determine a plurality of constellation pointsfor the respective transmitted spatial stream to estimate values for theconstellation points of other transmitted streams based at least in parton a suboptimal MIMO algorithm without looping over all possiblecombinations of the constellation points of the other transmittedstreams; code for determining a set of distance metrics as values of theplurality of constellation points for the respective transmitted spatialstream; and code for obtaining soft-decision outputs for respective bitsin the set of transmitted streams based on the distance metrics.
 45. Thenon-transitory computer-readable medium of claim 44, wherein the codefor utilizing the channel matrix and the sub-optimal MIMO algorithmincludes code for utilizing the channel matrix and the sub-optimal MIMOalgorithm based at least in part on Per-Stream List Detection (PSLD).46. The non-transitory computer-readable medium of claim 44, wherein thecode for utilizing the channel matrix and the sub-optimal MIMO algorithmincludes code for utilizing the channel matrix and the sub-optimal MIMOalgorithm based at least in part on Lattice-Reduced Detection (LRD). 47.The non-transitory computer-readable medium of claim 44, wherein thecode for utilizing the channel matrix and the sub-optimal MIMO algorithmincludes: code for utilizing the channel matrix and the sub-optimal MIMOalgorithm iteratively over the set of possible constellation points forthe respective transmitted stream in the set of transmitted streams toestimate candidate values for other transmitted streams in the set oftransmitted streams; and code for determining distance metrics at leastin part by selecting respective candidate values for the othertransmitted streams that minimize respective distance metrics for therespective transmitted stream over the set of possible constellationpoints.
 48. The non-transitory computer-readable medium of claim 44,further comprising code for processing the channel matrix based at leastin part on QR decomposition.
 49. The non-transitory computer-readablemedium of claim 44, wherein the code for obtaining soft-decision outputsincludes code for calculating log-likelihood ratios for respective bitsin the set of transmitted streams based on the distance metrics.
 50. Thenon-transitory computer-readable medium of claim 44, further comprising:code for storing initial distance metrics for the set of possibleconstellation points in a set of arrays that respectively correspond tothe set of transmitted streams, wherein the code for utilizing thechannel matrix and the sub-optimal MIMO algorithm includes: code foriterating over the respective transmitted stream to estimatecorresponding other transmitted streams and to determine correspondingdistance metrics; and code for storing a determined distance metric fora constellation point in an array corresponding to a transmitted streamor a corresponding estimated stream if the determined distance metric islower than a stored distance metric in the array for the constellationpoint.
 51. A multiple-input multiple-output (MIMO) receiving device forperforming low-complexity soft-output detection, comprising: aprocessor; memory in electronic communication with the processor;instructions stored in the memory, the instructions comprising: code forlooping over a set of transmitted spatial streams and for a respectivetransmitted spatial stream executing: code for determining a pluralityof constellation points for the respective transmitted spatial stream toestimate values for the constellation points of the other transmittedstreams based at least in part on a sub-optimal MIMO algorithm withoutlooping over all possible combinations of the constellation points ofthe other transmitted streams; code for determining a set of distancemetrics as values of the plurality of constellation points for therespective transmitted spatial stream; and code for obtaininghard-decision outputs for respective bits in the transmitted streamsbased on the distance metrics.
 52. The processor of claim 51, whereinthe instructions further comprise code for obtaining soft-decisionoutputs by calculating log-likelihood ratios for respective bits in thetransmitted streams based on the distance metrics.
 53. The processor ofclaim 51, wherein the code for determining the plurality ofconstellation points includes code for using the sub-optimal MIMOalgorithm based on at least one of Per-Stream List Detection,Lattice-Reduced Detection, a Guided-M algorithm, Zero Forcing, and aMinimum Mean Square Error algorithm.
 54. The processor of claim 53,wherein the instructions further comprise: code for performing QRdecomposition on a channel matrix that represents an effective MIMOchannel through which the transmitted streams are received, wherein thecode for determining one or more of the constellation points includescode for estimating other values and to determine corresponding distancemetrics using the channel matrix and the sub-optimal MIMO algorithm. 55.The processor of claim 53, wherein the code for determining one or moreof the constellation points includes: code for estimating other valuesand to determine corresponding distance metrics using the sub-optimalMIMO algorithm; code for comparing the determined corresponding distancemetrics to respective stored distance metrics for the transmittedstreams and estimated other values; and code for storing the determinedcorresponding distance metrics in place of respective stored distancemetrics that are higher than the determined corresponding distancemetrics.
 56. A method for generating soft-decision output values for aset of transmitted spatial streams in a communication system,comprising: looping over the set of transmitted spatial streams and fora respective transmitted spatial stream: determining a plurality ofconstellation points for the respective transmitted spatial stream toestimate values for the constellation points of the other transmittedstreams based at least in part on a single-input single-output (SISO)algorithm without looping over all possible combinations of theconstellation points of the other transmitted streams; determining a setof distance metrics as values of the plurality of constellation pointsfor the respective transmitted spatial stream; and generatingsoft-decision outputs for the respective transmitted stream based atleast in part on the set of distance metrics.
 57. The method of claim56, further comprising generating harddecision outputs for therespective transmitted stream based at least in part on the generatedsoft-decision outputs.
 58. The method of claim 56, further comprising:generating hard-decision outputs for the respective transmitted streamby searching for a minimum distance metric for a transmitted stream inrespective transmitted streams; and obtaining hard-decision outputs forthe transmitted stream and corresponding estimates for other transmittedstreams based at least in part on a reverse constellation mapping. 59.The method of claim 56, wherein the set of distance metrics comprisesoft-decision input values respectively representing estimated values ofthe transmitted spatial streams.
 60. The method of claim 59, wherein thesoft-decision input values are generated by a decoder using an outercode.